Dynamic probability of reinforcement for cooperation: Random game termination in the centipede game
Cooperation dies only when players see the end coming very soon and the chance of continuing keeps dropping.
01Research in Context
What this study did
Krockow et al. (2018) built a computer version of the centipede game. Two players take turns choosing to keep a growing pile of money or pass it on. Passing lets the pot grow, but the game can end at any time.
The team changed how likely the game was to end at each turn. Sometimes the chance stayed the same. Sometimes it dropped lower and lower. Neurotypical adults played many rounds while the computer tracked when they chose to quit.
What they found
People kept cooperating until almost the end in most rules. Only the dropping-probability rule made players quit early. When the expected game length shrank to just two turns, cooperation collapsed.
Exit points slid forward or back depending on how long players thought the game would last. The results show cooperation is fragile only when the horizon feels very short.
How this fits with other research
Fahmie et al. (2013) saw a similar quick shift with rats. When reinforcement odds changed, the rats’ response bias moved right away. Both studies show that choice follows the newest probability, even across species.
Storm (2000) found that schedule order changes the numbers you plug into Herrnstein’s matching law. Krockow’s team adds that order also changes where people stop cooperating. Together they warn: don’t assume parameters are stable across sessions.
Meltzer (1983) removed bias in pigeons by holding reinforcement ratios steady. Krockow’s work flips this idea: by letting the termination ratio drift, they created bias and watched cooperation fade.
Why it matters
If you run social-skills groups or token economies, remember that small schedule shifts can nudge sharing or turn-taking. A fading chance of “one more turn” can crash teamwork fast. State the horizon up front—"we’ll play five rounds"—to keep cooperation alive.
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02At a glance
03Original abstract
Experimental games have previously been used to study principles of human interaction. Many such games are characterized by iterated or repeated designs that model dynamic relationships, including reciprocal cooperation. To enable the study of infinite game repetitions and to avoid endgame effects of lower cooperation toward the final game round, investigators have introduced random termination rules. This study extends previous research that has focused narrowly on repeated Prisoner's Dilemma games by conducting a controlled experiment of two-player, random termination Centipede games involving probabilistic reinforcement and characterized by the longest decision sequences reported in the empirical literature to date (24 decision nodes). Specifically, we assessed mean exit points and cooperation rates, and compared the effects of four different termination rules: no random game termination, random game termination with constant termination probability, random game termination with increasing termination probability, and random game termination with decreasing termination probability. We found that although mean exit points were lower for games with shorter expected game lengths, the subjects' cooperativeness was significantly reduced only in the most extreme condition with decreasing computer termination probability and an expected game length of two decision nodes.
Journal of the Experimental Analysis of Behavior, 2018 · doi:10.1002/jeab.320